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Differentially Private High-Dimensional Approximate Range Counting, Revisited

Authors Martin Aumüller , Fabrizio Boninsegna , Francesco Silvestri

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Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
  • Mathematics of computing → Probabilistic algorithms
  • Security and privacy
Keywords
  • Differential Privacy
  • Locality Sensitive Filters
  • Approximate Range Counting
  • Concominant Statistics

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Abstract

Locality Sensitive Filters are known for offering a quasi-linear space data structure with rigorous guarantees for the Approximate Near Neighbor search (ANN) problem. Building on Locality Sensitive Filters, we derive a simple data structure for the Approximate Near Neighbor Counting (ANNC) problem under differential privacy (DP). Moreover, we provide a simple analysis leveraging a connection with concomitant statistics and extreme value theory. Our approach produces a simple data structure with a tunable parameter that regulates a trade-off between space-time and utility. Through this trade-off, our data structure achieves the same performance as the recent findings of Andoni et al. (NeurIPS 2023) while offering better utility at the cost of higher space and query time. In addition, we provide a more efficient algorithm under pure ε-DP and elucidate the connection between ANN and differentially private ANNC. As a side result, the paper provides a more compact description and analysis of Locality Sensitive Filters for Fair Near Neighbor Search, improving a previous result in Aumüller et al. (TODS 2022).

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Martin Aumüller, Fabrizio Boninsegna, and Francesco Silvestri. Differentially Private High-Dimensional Approximate Range Counting, Revisited. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 15:1-15:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FORC.2025.15

Author Details

Martin Aumüller
  • IT University of Copenhagen, Denmark
Fabrizio Boninsegna
  • Department of Information Engineering, University of Padova, Italy
Francesco Silvestri
  • Department of Information Engineering, University of Padova, Italy

Funding

This work was supported in part by the MUR PRIN 20174LF3T8 AHeAD project, by MUR PNRR CN00000013 National Center for HPC, Big Data and Quantum Computing, and by Marsden Fund (MFP-UOA2226).

Acknowledgements

The authors would like to thank Ninh Pham and Rasmus Pagh for useful discussions.

References

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